How the traverses are made
Each traverse starts as an invented loop of four to seven stations, lettered anticlockwise, with lines 30 to 320 m long. Lengths are booked to the centimetre or millimetre and angles to the minute or second (a compass to 15′). Small field errors are added so the precision lands between 1 in 2,000 and 1 in 10,000, as a tape or theodolite traverse would. Latitudes, departures and corrections are rounded to the last place booked, and a traverse is only used when every rounding is clear-cut and the rounded corrections add up exactly to the closing error.
A worked example
In set GATE45 (level 4, whole circle bearings, minutes), the five observed angles add up to 539° 58′, which is 2′ short of (2 × 5 − 4) × 90° = 540°. That is within the allowance of 1′ × √5, so each angle gains 24″. AB is 105° 47′; its back bearing, 285° 47′, plus the corrected angle at B (112° 47′ 24″) puts BC at 38° 34′ 24″. AB is 204.02 m long, so its latitude is −55.49 and its departure 196.33. The latitudes add up to +0.13 and the departures to −0.05: a closing error of √(0.13² + 0.05²) = 0.1393 m in 736.79 m, which is 1 in 5,290. By the Bowditch rule AB's latitude correction is −0.13 × 204.02 ÷ 736.79 = −0.04, and B lands at E 4132.30, N 6453.81. Open set GATE45
What each level asks
| Level | From the field book | You find |
|---|---|---|
| 1 Bearings | Fore bearings and lengths | Each bearing in the other style, back bearings, included angles and the (2n − 4) × 90° check |
| 2 Local attraction | Compass fore and back bearings to 15′ | The free line, the correction at each station, corrected bearings, included angles |
| 3 Closing error | Bearings and lengths | Latitudes, departures, closing error and its bearing, precision against 1 in 5,000 |
| 4 Bowditch | Included angles, lengths, one bearing, A's coordinates | Angular misclose, carried bearings, Gale's table, Bowditch corrections, coordinates |
| 5 Transit and area | Bearings and lengths | Transit rule corrections, then area from coordinates or by DMD |
| 6 Omitted | A line with its length or bearing missing, or two lengths missing | The missing values from the latitudes and departures of the other lines |
Questions
What is the difference between a whole circle bearing and a reduced bearing?
A whole circle bearing is measured clockwise from north, 0° to 360°. A reduced (quadrant) bearing is the angle from north or south, under 90°, with its quadrant: 120° 30′ WCB is S 59° 30′ E. In the SE quadrant subtract the WCB from 180°, in the SW subtract 180°, in the NW subtract it from 360°.
How do you correct local attraction in a compass traverse?
Find the line whose fore and back bearings differ by exactly 180°: both its stations are free. From there, work round the traverse. At each next station the corrected back bearing tells you the correction, and the same correction goes on the fore bearing read at that station.
How do you calculate latitude and departure?
Latitude = length × cos(bearing) and departure = length × sin(bearing). Latitudes are positive northwards and departures eastwards, so a line heading south-west has both negative. For a closed traverse both columns should add up to zero.
What is the Bowditch rule, and when is the transit rule used?
The Bowditch (compass) rule shares the closing error in proportion to each line's length: correction = −(Σ latitude) × length ÷ perimeter. The transit rule shares it in proportion to each latitude or departure and is meant for traverses whose angles are more precise than their lengths.
How do you find the closing error and precision of a traverse?
The closing error is √(ΣL² + ΣD²), from the sums of the latitudes and departures. The precision is 1 in N, where N is the perimeter divided by the closing error: 736.74 m with a 0.14 m error is about 1 in 5,260. The allowable value is set by the course or specification.
How do you find the area of a closed traverse?
From coordinates, twice the area is the sum of E of each station times N of the next, minus E of the next times N of that station. With double meridian distances, the first DMD is the first departure, each next DMD adds the previous and own departures, and the area is half the sum of DMD × latitude.
How do you solve omitted measurements in a traverse?
Add up the latitudes and departures of the lines you know. The missing line closes the traverse, so its latitude and departure are those sums with the signs changed; its length and bearing follow. Two missing lengths give two equations, one for latitudes and one for departures.
Sources, checked October 26, 2026: B. R. Harvey, Survey Computations, UNSW (version 20 July 2023, PDF), chapter 4: Bowditch and transit rules, linear misclose and 1 in N, worked traverses; NPTEL, Surveying (IIT Roorkee), example 19-2: local attraction and included angles; NPTEL lessons 29 to 31: consecutive coordinates, error of closure, Bowditch and transit methods, Gale's traverse table, omitted measurements; Achievable FE Civil, Surveying: area by double meridian distances.